{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T14:42:29Z","timestamp":1773412949569,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,10,28]],"date-time":"2014-10-28T00:00:00Z","timestamp":1414454400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1007\/s10957-014-0667-7","type":"journal-article","created":{"date-parts":[[2014,10,27]],"date-time":"2014-10-27T17:49:05Z","timestamp":1414432145000},"page":"296-325","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Optimization of Cytostatic Leukemia Therapy in an Advection\u2013Reaction\u2013Diffusion Model"],"prefix":"10.1007","volume":"167","author":[{"given":"Chahrazed","family":"Benosman","sequence":"first","affiliation":[]},{"given":"Bedr\u2019Eddine","family":"A\u00efnseba","sequence":"additional","affiliation":[]},{"given":"Arnaud","family":"Ducrot","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,10,28]]},"reference":[{"key":"667_CR1","doi-asserted-by":"crossref","first-page":"2019","DOI":"10.1016\/j.ejca.2006.06.005","volume":"42","author":"JWW Coebergh","year":"2006","unstructured":"Coebergh, J.W.W., Reedijk, A.M.J., de Vries, E., Martos, C., Jakab, Z., Steliarova-Foucher, E., Kamps, W.A.: Leukaemia incidence and survival in children and adolescents in Europe during 1978\u20131997. Report from the Automated Childhood Cancer Information System Project. Eur. J. Cancer 42, 2019\u20132036 (2006)","journal-title":"Eur. J. Cancer"},{"key":"667_CR2","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.bcmd.2003.10.005","volume":"32","author":"GB Segel","year":"2004","unstructured":"Segel, G.B., Lichtman, M.A.: Familial (inherited) leukemia, lymphoma, and myeloma: an overview. Blood Cells Mol. Dis. 32, 246\u2013261 (2004)","journal-title":"Blood Cells Mol. Dis."},{"key":"667_CR3","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1007\/s00285-010-0360-x","volume":"62","author":"B A\u00efnseba","year":"2011","unstructured":"A\u00efnseba, B., Benosman, C.: Global dynamics of hematopoietic stem cells and differentiated cells in a chronic myeloid leukemia model. J. Math. Biol. 62, 975\u2013997 (2011)","journal-title":"J. Math. Biol."},{"key":"667_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2011\/104631","volume":"2011","author":"H Reikvam","year":"2011","unstructured":"Reikvam, H., Hatfield, K.J., Kittang, A.O., Hovland, R.: Bruserud, \u00d8: acute myeloid leukemia with the t(8;21) translocation: clinical consequences and biological implications. J. Biomed. Biotechnol. 2011, 1\u201323 (2011)","journal-title":"J. Biomed. Biotechnol."},{"key":"667_CR5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1053\/j.seminhematol.2008.09.010","volume":"46","author":"KM Bernt","year":"2009","unstructured":"Bernt, K.M., Armstrong, S.A.: Leukemia stem cells and human acute lymphoblastic leukemia. Semin. Hematol. 46, 33\u201338 (2009)","journal-title":"Semin. Hematol."},{"key":"667_CR6","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.semcancer.2009.12.001","volume":"20","author":"SW Lane","year":"2010","unstructured":"Lane, S.W., Gilliland, D.G.: Leukemia stem cells. Semin. Cancer Biol. 20, 71\u201376 (2010)","journal-title":"Semin. Cancer Biol."},{"key":"667_CR7","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.critrevonc.2010.11.006","volume":"80","author":"F Marchesi","year":"2011","unstructured":"Marchesi, F., Annibali, O., Cerchiara, E., Tirindelli, M.C., Avvisati, G.: Cytogenetic abnormalities in adult non-promyelocytic acute myeloid leukemia: a concise review. Crit. Rev. Oncol. Hematol. 80, 331\u2013346 (2011)","journal-title":"Crit. Rev. Oncol. Hematol."},{"key":"667_CR8","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.bbrc.2009.03.127","volume":"383","author":"H Yamazaki","year":"2009","unstructured":"Yamazaki, H., Nishida, H., Iwata, S., Dang, N.H., Morimoto, C.: CD90 and CD110 correlate with cancer stem cell potentials in human T-acute lymphoblastic leukemia cells. Biochem. Biophys. Res. Commun. 383, 172\u2013177 (2009)","journal-title":"Biochem. Biophys. Res. Commun."},{"key":"667_CR9","unstructured":"Prenkert, M.: On mechanisms of drug resistance in acute myeloid leukemia. P\u00d6rebro University, thesis. ISBN 978-91-7668-729-1 (2010)"},{"key":"667_CR10","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1182\/blood-2003-12-4266","volume":"104","author":"AB Dietz","year":"2004","unstructured":"Dietz, A.B., Souan, L., Knutson, G.J., Bulur, P.A., Litzow, M.R., Vuk-Pavlovi\u0107, S.: Imatinib mesylate inhibits T-cell proliferation in vitro and delayed-type hypersensitivity in vivo. Blood 104, 1094\u20131099 (2004)","journal-title":"Blood"},{"key":"667_CR11","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1056\/NEJMra013339","volume":"346","author":"DG Savage","year":"2002","unstructured":"Savage, D.G., Antman, K.H.: Imatinib mesylate: a new oral targeted therapy. Drug therapy. N. Engl. J. Med. 346, 683\u2013693 (2002)","journal-title":"N. Engl. J. Med."},{"key":"667_CR12","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.blre.2010.09.004","volume":"25","author":"M Paganin","year":"2011","unstructured":"Paganin, M., Ferrando, A.: Molecular pathogenesis and targeted therapies for NOTCH1-induced T-cell acute lymphoblastic leukemia. Blood Rev. 25, 83\u201390 (2011)","journal-title":"Blood Rev."},{"key":"667_CR13","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.beha.2006.11.006","volume":"20","author":"RM Stone","year":"2007","unstructured":"Stone, R.M.: Targeted agents in AML: much more to do. Best Pract. Res. Clin. Haematol. 20, 39\u201348 (2007)","journal-title":"Best Pract. Res. Clin. Haematol."},{"key":"667_CR14","first-page":"1","volume":"7","author":"W Ma","year":"2012","unstructured":"Ma, W., Gutierrez, A., Goff, D.J., Geron, I., Sadarangani, A., Jamieson, C.A.M., Court, A.C., Shih, A.Y., Jiang, Q., Wu, C.C., Li, K., Smith, K.M., Crews, L.A., Gibson, N.W., Deichaite, I., Morris, S.R., Wei, P., Carson, D.A., Look, A.T., Jamieson, C.H.M.: Notch1 signaling promotes human T-cell acute lymphoblastic leukemia initiating cell regeneration in supportive niches. Plos One 7, 1\u201314 (2012)","journal-title":"Plos One"},{"key":"667_CR15","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s00285-007-0132-4","volume":"56","author":"A Kettemann","year":"2008","unstructured":"Kettemann, A., Neuss-Radu, M.: Derivation and analysis of a system modeling the chemotactic movement of hematopoietic stem cells. J. Math. Biol. 56, 579\u2013610 (2008)","journal-title":"J. Math. Biol."},{"key":"667_CR16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s00285-010-0369-1","volume":"63","author":"V Andasari","year":"2011","unstructured":"Andasari, V., Gerisch, A., Lolas, G., South, A.P., Chaplain, M.J.: Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. J. Math. Biol. 63, 141\u2013171 (2011)","journal-title":"J. Math. Biol."},{"key":"667_CR17","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.plrev.2009.10.002","volume":"6","author":"V Volpert","year":"2009","unstructured":"Volpert, V., Petrovskii, S.: Reaction\u2013diffusion waves in biology. Phys. Life Rev. 6, 267\u2013310 (2009)","journal-title":"Phys. Life Rev."},{"key":"667_CR18","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1051\/mmnp\/20094302","volume":"4","author":"J Clairambault","year":"2009","unstructured":"Clairambault, J.: Modelling physiological and pharmacological control on cell proliferation to optimise cancer treatments. Math. Model. Nat. Phenom. 4, 12\u201367 (2009)","journal-title":"Math. Model. Nat. Phenom."},{"key":"667_CR19","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1051\/mmnp:2007005","volume":"2","author":"A Ducrot","year":"2007","unstructured":"Ducrot, A., Volpert, V.: On a model of leukemia development with a spatial cell distribution. Math. Model. Nat. Phenom. 2, 101\u2013120 (2007)","journal-title":"Math. Model. Nat. Phenom."},{"key":"667_CR20","first-page":"315","volume":"4","author":"TI Mughal","year":"2010","unstructured":"Mughal, T.I., Schrieber, A.: Principal long-term adverse effects of imatinib in patients with chronic myeloid leukemia in chronic phase. Biologics 4, 315\u2013323 (2010)","journal-title":"Biologics"},{"key":"667_CR21","doi-asserted-by":"crossref","first-page":"5151","DOI":"10.1182\/blood-2006-09-046144","volume":"109","author":"JL Harousseau","year":"2007","unstructured":"Harousseau, J.L., Lancet, J.E., Reiffers, J., Lowenberg, B., Thomas, X., Huguet, F., Fenaux, P., Zhang, S., Rackoff, W., De Porre, P., Stone, R.: A phase 2 study of the oral farnesyltransferase inhibitor tipifarnib in patients with refractory or relapsed acute myeloid leukemia. Blood 109, 5151\u20135156 (2007)","journal-title":"Blood"},{"key":"667_CR22","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1038\/sj.bjc.6603310","volume":"95","author":"LH Abbott","year":"2006","unstructured":"Abbott, L.H., Michor, F.: Mathematical models of targeted cancer therapy. Br. J. Cancer 95, 1136\u20131141 (2006)","journal-title":"Br. J. Cancer"},{"key":"667_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2012\/270425","volume":"2012","author":"K Chotinantakul","year":"2012","unstructured":"Chotinantakul, K., Leeanansaksiri, W.: Hematopoietic stem cell development, niches, and signaling pathways. Bone Marrow Res. 2012, 1\u201316 (2012)","journal-title":"Bone Marrow Res."},{"key":"667_CR24","doi-asserted-by":"crossref","unstructured":"Tajbakhsh, S.: Stem cell: what\u2019s in a name? Nat. Rep. Stem Cells (2009). doi: 10.1038\/stemcells.2009.90","DOI":"10.1038\/stemcells.2009.90"},{"key":"667_CR25","volume-title":"Cell Proliferation, Differentiation, and Apoptosis. Holland-Frei Cancer Medicine","author":"M Andreeff","year":"2000","unstructured":"Andreeff, M., Goodrich, D.W., Pardee, A.B.: Cell Proliferation, Differentiation, and Apoptosis. Holland-Frei Cancer Medicine, 5th edn. BC Decker, Hamilton (2000)","edition":"5"},{"key":"667_CR26","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1002\/sapm1972514317","volume":"52","author":"HP Greenspan","year":"1972","unstructured":"Greenspan, H.P.: Models for the growth of a solid tumor by diffusion. Stud. Appl. Math. 52, 317\u2013340 (1972)","journal-title":"Stud. Appl. Math."},{"key":"667_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-4178-6","volume-title":"Mathematical Methods and Models in Biomedicine","author":"U Ledzewicz","year":"2013","unstructured":"Ledzewicz, U., Sch\u00e4ttler, H., Friedman, A., Kashdan, E.: Mathematical Methods and Models in Biomedicine. Springer, Heidelberg (2013)"},{"key":"667_CR28","first-page":"143","volume":"01","author":"I Demin","year":"2010","unstructured":"Demin, I., Ducrot, A., Volpert, V.: Spatial distribution of cell populations in the process of erythropoiesis. Int. Electron. J. Pure Appl. Math. 01, 143\u2013161 (2010)","journal-title":"Int. Electron. J. Pure Appl. Math."},{"key":"667_CR29","doi-asserted-by":"crossref","first-page":"2835","DOI":"10.1002\/stem.1184","volume":"12","author":"K Cheng","year":"2012","unstructured":"Cheng, K., Shen, D., Xie, Y., Cingolani, E., Malliaras, K., Marb\u00e0n, E.: Brief report: mechanism of extravasation of infused stem cells. Stem Cells 12, 2835\u20132842 (2012)","journal-title":"Stem Cells"},{"key":"667_CR30","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1038\/35102167","volume":"414","author":"T Reya","year":"2001","unstructured":"Reya, T., Morrison, S.J., Clarke, M.F., Weissman, I.L.: Stem cells, cancer, and cancer stem cells. Nature 414, 105\u2013111 (2001)","journal-title":"Nature"},{"key":"667_CR31","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1038\/nrc3080","volume":"11","author":"D Wirtz","year":"2011","unstructured":"Wirtz, D., Konstantopoulos, K., Searson, P.C.: The physics of cancer: the role of physical interactions and mechanical forces in metastasis. Nat. Rev. Cancer 11, 512\u2013522 (2011)","journal-title":"Nat. Rev. Cancer"},{"key":"667_CR32","first-page":"4771","volume":"26","author":"V Ferraresi","year":"2006","unstructured":"Ferraresi, V., Catrical\u00e0, C., Ciccarese, M., Ferrari, A., Zeuli, M., Cognetti, F.: Severe skin reaction in a patient with gastrointestinal stromal tumor treated with imatinib mesylate. Anticancer Res. 26, 4771\u20134774 (2006)","journal-title":"Anticancer Res."},{"key":"667_CR33","doi-asserted-by":"crossref","first-page":"S83","DOI":"10.1016\/S0959-8049(02)80608-6","volume":"38","author":"AT Oosterom Van","year":"2002","unstructured":"Van Oosterom, A.T., Judson, I.R., Verweij, J., Stroobants, S., Dumez, H., Donato di Paola, E., Sciot, R., Van Glabbeke, M., Dimitrijevic, S., Nielsen, O.S.: Update of phase I study of imatinib (STI571) in advanced soft tissue sarcomas and gastrointestinal stromal tumors: a report of the EORTC Soft Tissue and Bone Sarcoma Group. Eur. J. Cancer 38, S83\u2013S87 (2002)","journal-title":"Eur. J. Cancer"},{"key":"667_CR34","doi-asserted-by":"crossref","first-page":"151","DOI":"10.3934\/mbe.2013.10.151","volume":"10","author":"E Fimmel","year":"2013","unstructured":"Fimmel, E., Semenov, Y.S., Bratus, A.S.: On optimal and suboptimal treatment strategies for a mathematical model of leukemia. Math. Biosci. Eng. 10, 151\u2013165 (2013)","journal-title":"Math. Biosci. Eng."},{"key":"667_CR35","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1137\/S0036139998338509","volume":"60","author":"KR Fister","year":"2000","unstructured":"Fister, K.R., Panetta, J.C.: Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math. 60, 1059\u20131072 (2000)","journal-title":"SIAM J. Appl. Math."},{"key":"667_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-9221-6","volume-title":"Abstract Linear Theory, Linear and Quasilinear Parabolic Problems","author":"H Amann","year":"1995","unstructured":"Amann, H.: Abstract Linear Theory, Linear and Quasilinear Parabolic Problems. Birkhauser, Basel (1995)"},{"key":"667_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5561-1","volume-title":"Semigroups of Linear Operators and Applications to Partial Differential Equations","author":"A Pazy","year":"1983","unstructured":"Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)"},{"key":"667_CR38","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1080\/03605309708821314","volume":"22","author":"H Hieber","year":"1997","unstructured":"Hieber, H., Pr\u00fcss, J.: Heat kernels and maximal $$L^p-L^q$$ L p - L q estimates for parabolic evolution equations. Commun. Partial Differ. Equ. 22, 1647\u20131669 (1997)","journal-title":"Commun. Partial Differ. Equ."},{"key":"667_CR39","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8570-6","volume-title":"Evolutionary Integral Equations and Applications","author":"J Pr\u00fcss","year":"1993","unstructured":"Pr\u00fcss, J.: Evolutionary Integral Equations and Applications. Birkhauser, Basel (1993)"},{"key":"667_CR40","volume-title":"Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics No. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics No. 840","author":"D Henry","year":"1981","unstructured":"Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics No. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics No. 840. Springer, Berlin (1981)"},{"key":"667_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1021865709529","volume":"102","author":"V Barbu","year":"1999","unstructured":"Barbu, V., Iannelli, M.: Optimal control of population dynamics. J. Optim. Theory Appl. 102, 1\u201314 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"667_CR42","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.jmaa.2011.11.069","volume":"388","author":"B A\u00efnseba","year":"2012","unstructured":"A\u00efnseba, B., Bendahmane, M., Ruiz-Baier, R.: Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology. J. Math. Anal. Appl. 388, 231\u2013247 (2012)","journal-title":"J. Math. Anal. Appl."},{"key":"667_CR43","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1016\/j.aml.2011.01.043","volume":"24","author":"D Picart","year":"2011","unstructured":"Picart, D., A\u00efnseba, B., Milner, F.: Optimal control problem on insect pest populations. Appl. Math. Lett. 24, 1160\u20131164 (2011)","journal-title":"Appl. Math. Lett."},{"key":"667_CR44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3389\/fonc.2013.00082","volume":"3","author":"IA Rodriguez-Brenes","year":"2013","unstructured":"Rodriguez-Brenes, I.A., Wodarz, D., Komarova, N.L.: Stem cell control, oscillations, and tissue regeneration in spatial and non-spatial models. Front. Oncol. 3, 1\u201310 (2013)","journal-title":"Front. Oncol."},{"key":"667_CR45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2011\/396076","volume":"2011","author":"S Moore","year":"2011","unstructured":"Moore, S., Lyle, S.: Quiescent, slow-cycling stem cell populations in cancer: a review of the evidence and discussion of significance. J. Oncol. 2011, 1\u201311 (2011)","journal-title":"J. Oncol."},{"key":"667_CR46","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.mbs.2011.09.005","volume":"234","author":"M Sehl","year":"2011","unstructured":"Sehl, M., Zhou, H., Sinsheimer, J.S., Lange, K.L.: Extinction models for cancer stem cell therapy. Math. Biosci. 234, 132\u2013146 (2011)","journal-title":"Math. Biosci."},{"key":"667_CR47","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.ccr.2013.01.026","volume":"23","author":"S Takeishi","year":"2013","unstructured":"Takeishi, S., Matsumoto, A., Onoyama, I., Naka, K., Hirao, A., Nakayama, K.I.: Ablation of Fbxw7 eliminates leukemia-initiating cells by preventing quiescence. Cancer Cell 23, 347\u2013361 (2013)","journal-title":"Cancer Cell"},{"key":"667_CR48","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1051\/mmnp\/20105304","volume":"5","author":"C Calmelet","year":"2010","unstructured":"Calmelet, C., Prokop, A., Mensah, J., McCawley, L.J., Crooke, P.S.: Modeling the cancer stem cell hypothesis. Math. Model. Nat. Phenom. 5, 40\u201362 (2010)","journal-title":"Math. Model. Nat. Phenom."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-014-0667-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-014-0667-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-014-0667-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,26]],"date-time":"2020-08-26T05:08:40Z","timestamp":1598418520000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-014-0667-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,28]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["667"],"URL":"https:\/\/doi.org\/10.1007\/s10957-014-0667-7","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,28]]}}}